# Homework Help: Basic Energy and Time Uncertainty Problem

1. Oct 31, 2012

### ElijahRockers

1. The problem statement, all variables and given/known data

A pi zero meson is an unstable particle produced in high energy particle collisions. It has a mass-energy equivalent of about 135MeV, and it exists for an average life-time of only 8.7x10^-17 seconds before decaying into two gamma rays. Using the uncertainty principle, estimate the fractional uncertainty Δm/m in its mass determination.

3. The attempt at a solution

Ok,

I know mc^2 = 135 MeV = 2.16x10^-11 J
Δt = 8.7x10-17 s

And I suspect I am supposed to use ΔtΔE ≥ h/(4pi)

Taking a wild stab in the dark here based off of some examples I've looked at:

ΔE/E = Δm/m ?

if so, I am given E, and the time-energy uncertainty equation will give me ΔE, so I can calculate Δm/m

only I'm getting the wrong answer.

This question is addressed in a previous thread, located here, where Javier suggests using ΔEΔt = h/2pi instead of h/4pi

When I use this method to calculate ΔE, then use ΔE/E = Δm/m, I get the correct answer.

Why do I have to use h/2pi instead of h/4pi?

2. Nov 1, 2012

### haruspex

As I understand it, the usual formulation of the uncertainty inequality is ΔfΔg ≥ ℏ/2. Since ℏ = h/2π, that's h/4π.

3. Nov 1, 2012

### ElijahRockers

Yeah. but if you check the thread I linked to, someone says in this instance he should use ℏ instead of ℏ/2. i used it, and it gave me the correct answer. I'm just not sure why